Universal Axiomatization of the Binary Excluded Middle Law and the Dual Ontology-Cognition Entropy System — A Fundamental Framework for Unified Observation Theory
Addressing cross-disciplinary fundamental issues including paradigm separation between classical and quantum observation, logical drift in general artificial intelligence probabilistic frameworks, and ambiguous uncertainty tracing in information systems, this study proposes a universal axiomatic framework of the binary excluded middle law and establishes a dual theoretical architecture consisting of ontology entropy and cognitive entropy. Strict logical demonstration verifies that all objective physical systems, regardless of microscopic or macroscopic scale, obey binary exclusive truth-value constraints without inherent superposition states or intrinsic probabilistic uncertainty. Phenomena such as quantum superposition, observational fuzziness, and probabilistic ambiguity are cognitive representations arising from information isolation and insufficient observational coupling, rather than inherent ontological properties of physical systems. This study redefines the essential nature of observation as a threshold-induced phase transition process, in which continuous information aggregation reduces cognitive entropy and eventually drives the system toward a deterministic binary steady state. Under this dual-entropy paradigm, the Schrödinger’s cat superposition paradox is fully and self-consistently resolved, eliminating long-standing logical ambiguities in quantum observation interpretation. This paper further conducts cross-domain adaptability analysis and constructs a unified fundamental logical framework for physical observation, intelligent cognition, information evaluation, and numerical computation, while outlining a phased systematic research roadmap. The results indicate that the binary excluded middle law serves as a universal underlying logical meta-rule for natural and intelligent information systems. The proposed dual ontology–cognitive entropy system fundamentally unifies the paradigms of classical and quantum physics, natural science, and artificial intelligence, possessing significant fundamental theoretical innovative value and broad engineering application prospects.
Addressing cross-disciplinary fundamental issues including paradigm separation between classical and quantum observation, logical drift in general artificial intelligence probabilistic frameworks, and ambiguous uncertainty tracing in information systems, this study proposes a universal axiomatic framework of the binary excluded middle law and establishes a dual theoretical architecture consisting of ontology entropy and cognitive entropy. Strict logical demonstration verifies that all objective physical systems, regardless of microscopic or macroscopic scale, obey binary exclusive truth-value constraints without inherent superposition states or intrinsic probabilistic uncertainty. Phenomena such as quantum superposition, observational fuzziness, and probabilistic ambiguity are cognitive representations arising from information isolation and insufficient observational coupling, rather than inherent ontological properties of physical systems. This study redefines the essential nature of observation as a threshold-induced phase transition process, in which continuous information aggregation reduces cognitive entropy and eventually drives the system toward a deterministic binary steady state. Under this dual-entropy paradigm, the Schrödinger’s cat superposition paradox is fully and self-consistently resolved, eliminating long-standing logical ambiguities in quantum observation interpretation. This paper further conducts cross-domain adaptability analysis and constructs a unified fundamental logical framework for physical observation, intelligent cognition, information evaluation, and numerical computation, while outlining a phased systematic research roadmap. The results indicate that the binary excluded middle law serves as a universal underlying logical meta-rule for natural and intelligent information systems. The proposed dual ontology–cognitive entropy system fundamentally unifies the paradigms of classical and quantum physics, natural science, and artificial intelligence, possessing significant fundamental theoretical innovative value and broad engineering application prospects.
This comprehensive interdisciplinary investigation synthesizes six foundational domains in modern physics and computer science: quantum vacuum dynamics, quantum measurement theory, binary computation architecture, artificial intelligence evolution, relativistic temporal structure, and quantum entanglement phenomena. Quantum vacuum—far from representing absolute emptiness—exhibits continuous zero-point energy fluctuations generating virtual particle-antiparticle pairs via Heisenberg uncertainty principle, with Casimir effect providing experimental verification through measurable attractive force (F/A = -ℏcπ²/240d⁴) between conducting plates. Schrödinger's cat paradox illustrates quantum superposition collapse upon measurement, revealing observer-dependent reality contradicting classical determinism and motivating interpretational frameworks including Copenhagen collapse, many-worlds branching, and decoherence mechanisms. Binary computation architecture—utilizing base-2 representation (0,1 states)—exploits transistor switching characteristics enabling universal information encoding, with von Neumann architecture establishing stored-program paradigm foundational to modern computing. Artificial intelligence evolved from Turing's universal computation and symbolic reasoning systems through connectionist neural networks to contemporary deep learning architectures achieving superhuman performance in pattern recognition, natural language processing, and strategic game-playing domains. Einstein's special relativity demonstrates temporal relativity through velocity-dependent time dilation (τ = τ₀√(1-v²/c²)) and general relativity's gravitational time dilation near massive objects, with GPS satellite corrections providing daily experimental confirmation. Quantum entanglement—non-local correlation between spatially separated particles violating Bell inequalities—enables quantum information protocols including quantum cryptography, quantum teleportation, and quantum computation while challenging classical notions of locality and realism. The synthesis reveals deep connections: quantum vacuum provides cosmological initial conditions for universal genesis; measurement problem connects consciousness to physical reality; binary architecture enables AI substrate; relativistic effects constrain information transmission; and entanglement enables novel computational paradigms transcending classical limits.
The core dilemma of modern physics stems from two unproven ontological presuppositions: that spacetime is an innate container preceding matter, and that matter is an entity composed of indivisible particles. These presuppositions have led to the fundamental split between general relativity and quantum mechanics, giving rise to a series of century-old unsolved problems such as wave-particle duality, the quantum measurement paradox, the nature of gravity, and dark matter and dark energy. Based on the sole unfalsifiable first principle that "the essence of cognition is succession", this paper deduces a complete ontological system through pure a priori reasoning: the authentic physical world consists solely of one-dimensional successive rays and their transverse coupling relations; time is the successive extension of rays, space is the network of coupling relations, matter is the steady state of closed coupling, and all interactions are different manifestations of coupling actions. Particles are not authentically existing entities, but rather point-like endpoint phenomena presented in the observer's phenomenal world when two rays undergo an all-or-nothing coupling. Based on this framework, this paper uniformly explains all core phenomena in both the microscopic quantum domain and the macroscopic relativistic domain in one go, resolves all traditional physical paradoxes at the ontological level, achieves the ontological unification of the four fundamental forces, and proposes three falsifiable core predictions. This paper demonstrates that all theories of traditional physics are approximate descriptions of the authentic physical world at the phenomenal level, and their fundamental error lies in mistaking "coupling endpoints" for "primitive entities", thereby reversing the causal relationship. Cognitive Succession Ontology provides a logically consistent and universally unified ultimate foundation for physics.
The unmediated, instantaneous long-range correlation demonstrated by quantum entanglement has been repeatedly confirmed by experiments, yet it forms an irreconcilable logical paradox with humanity’s fundamental understanding of cosmic scale, spatial separation, and cognitive limitations. If entanglement is acknowledged to possess infinite, universal action capacity, it would lead to the extreme conclusion that humans could directly reach the boundaries of the universe and connect with the entire cosmos through microscopic quantum phenomena—a notion entirely at odds with the reality that humanity has yet to escape the solar system and remains largely ignorant of the vast majority of the universe. Through rigorous logical deduction, this paper proposes the only self-consistent dual possibilities: first, quantum entanglement may possess undiscovered physical limitations, with its nonlocal properties effective only within a finite scale; second, modern physics may harbor fundamental cognitive biases regarding the nature of space, the meaning of distance, and the reality of separation, suggesting that space is not an objective, independent foundational physical entity. This paper systematically demonstrates the rationality, self-consistency, and revolutionary implications of these two possibilities for physics and cosmology, offering a novel theoretical framework to resolve the underlying conflict between quantum mechanics and cosmology.
Classical information theory and quantum information theory are respectively based on Boolean algebra and Hilbert space projection lattices, lacking a unified logical framework for cross-scale physical propositions covering classical, mesoscopic and quantum domains. Traditional physics attributes the classical-quantum transition to continuous spatial scale variation, which is essentially external parameter determinism and cannot explain the peculiar intermediate characteristics of mesoscopic systems. This paper constructs the philosophical and mathematical foundation of mesoscopic information theory based on the coupling of S4 modal logic and the non-distributive modular lattice M₃. A composite axiom system is proposed, and Axiom 3 (a–g) realizes the consistent embedding of S4 modal operators on non-distributive lattices. The cross-scale evolution of physical systems is reinterpreted as discrete phase transition of propositional lattice types, with an endogenous CHSH-type correlation threshold τ≈2.414 serving as the operational criterion for mesoscopic phase. A Möbius-weighted lattice entropy independent of Shannon and von Neumann entropy is established to characterize structural information of mesoscopic logical systems. Noise and decoherence are redefined as intrinsic signals of lattice structural transition rather than simple information dissipation. This study establishes the independent ontological status of mesoscopic propositional systems, breaks the scale-phenomenological paradigm in traditional cross-scale physics, and provides a new foundational framework for the unification of cross-scale information theory.
This paper proposes a quantum measurement framework based on structuralstability theory, aiming to resolve the logical dilemma of the quantum–classicaltransition in Schrödinger’s cat paradox. Traditional quantum mechanics relies onexternal mechanisms such as “observer introduction” or “decoherence” to explainmacroscopic reality, leading to vague ontological commitments. We argue that thefundamental reason macroscopic quantum states cannot maintain coherent superpositions lies in the self-organizing critical behavior constrained by the system’sinternal structural stability. The core mechanism is: when a quantum system couples with a classical measuring device, its Hilbert space representation is forced toproject from a high-dimensional unitary representation onto a low-dimensional classical representation, a process driven by the extremization of a structural stabilityfunctional, not by external observation. We rigorously prove that when the system’sstructural information density exceeds a critical threshold, the quantum superposition state cannot satisfy self-consistency constraints mathematically; the systemmust select a classical eigenstate through an “algebraic filtration” mechanism. Thetheory yields three testable predictions: (1) a microscopic entropy production pulseat the moment of coupling between the measuring device and the quantum system,of order 10−21 J/K; (2) a deviation of the quantum Zeno suppression factor fromstandard quantum mechanical predictions on microsecond scales; (3) a scaling-lawdivergence of the decoherence time of macroscopic superpositions at critical parameters. These effects can be tested in coupled superconductor qubit–mechanicalresonator systems. The framework does not modify unitary evolution, does not relyon many-worlds assumptions, and does not introduce collapse postulates; instead,it transforms the measurement problem into a question of compatibility betweenquantum information structure and geometric–topological constraints.
This paper, based on two fundamental physical axioms—Information Conservation (A1) and Computability (A2)—systematically argues for the intrinsic logical structure necessary for describing physical reality. Research shows that in aself-referential universe model constrained by local observations, the truth-valuejudgment logic of physical propositions necessarily deviates from classical Booleanlogic. The core root lies in the “local-global inequivalence” of physical systems: theinformation contained in the global physical state cannot be completely determinedby any finite observational procedure within a finite spacetime region. This leads tothe invalidity of the law of excluded middle within the system, and consequently,the logical structure mathematically manifests as a non-distributive orthomodularlattice, i.e., Birkhoff–von Neumann quantum logic. This structure is proven tocorrespond exactly to the subobject lattice in the ∞-topos TA constructed previously. This theoretical framework finally leads to a testable cosmological prediction:the central value of the non-Gaussianity parameter fNL of the cosmic microwavebackground (CMB) temperature fluctuations is about −3.2. Next-generation CMBexperiments (such as CMB-S4) will be able to test this prediction precisely, andthe results can be used to evaluate whether the quantum logical structure emergingfrom the basic axioms is suitable for describing the real universe.